DBA is De Bellis Antiquitatus, wargame rules for ancient and medieval tabletop battles.
So what's a wargame and how does it relate to a tabletop?
A wargame (setting aside the ancient history) is a game where some kind of army is set against some other kind of army. Typically each side is controlled by a single player, though there are any amount of variations: and the results are partly ruled by chance and partly by what the rules say about one type of force's capabilities against the other.
"Tabletop" means that all this happens in a physical environment with pieces you can touch, normally on a wargame table with opponents face-to-face with each other.